A148828 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, -1), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 27, 85, 320, 1131, 4406, 16309, 66319, 257631, 1059441, 4209231, 17719241, 72257735, 305974740, 1264251256, 5432841123, 22812307631, 98420594164, 416837449309, 1816519187679, 7778083186221, 33995667489784, 146452230523412, 644764972171668, 2799708134506806, 12354221552659051

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148825 A148826 A148827 * A148829 A148830 A148831

Adjacent sequences: A148825 A148826 A148827 * A148829 A148830 A148831

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved